Worksheet 4: Conservation of Momentum II - Modeling Physics

Impulsive Force Model Worksheet 4:
Conservation of Momentum II
1. Old cannons were built on wheeled carts, both to facilitate moving the cannon and to allow the
cannon to recoil when fired. When a 150 kg cannon and cart recoils at 1.5 m/s, at what velocity would
a 10 kg cannonball leave the cannon
a. Complete a conservation of momentum diagram for firing one of these cannons.
event:
initial
final
mass/object/velocity
mass/object/velocity
- 0 +
Momentum conservation equation:
b. Momentum conservation equation:
- 0 +
c. Find the velocity of the cannonball.
2. On an icy road, a 5000 kg truck rear-ends a 1200 kg car that had been traveling at 13 m/s, causing
the truck to slow from 14 m/s to 12 m/s and the car to speed up.
a. Complete the momentum conservation diagram for the accident.
event:
initial
final
mass/object/velocity
mass/object/velocity
- 0 +
Momentum conservation equation:
b. Momentum conservation equation:
- 0 +
c. Find the final velocity of the car.

3. During alpha decay, an atom ejects two protons and two neutrons (an alpha particle, which is also a
helium nucleus). When radium-226 decays, it becomes radon-222 by ejecting an alpha particle.
a. Complete the momentum conservation diagram for the radioactive decay of radium-226.
(Recall from chemistry that the isotopic number of an element is related to its mass.)
initial
mass/object/velocity
event:
final
mass/object/velocity
- 0 +
Momentum conservation equation:
b. Momentum conservation equation:
- 0 +
c. How many times larger will the final velocity of the alpha particle be compared to the final
velocity of the radon-222
4. An apple falls from a tree.
a. Complete a qualitative conservation of momentum diagram where the apple is initially
attached to the tree and the final situation is just before the apple hits the ground.
initial
mass/object/velocity
event:
final
mass/object/velocity
- 0 +
Momentum conservation equation:
b. Momentum conservation equation:
- 0 +

5. Airplanes maneuver on the
ground by using thrust from their
jets or propellers. A fully loaded,
396,900 kg Boeing 747-400 gets a
total of 1100 kiloNewtons of thrust
from its jet engines. (Data from
Boeing's website.) Takeoff speed
depends on a number of factors like
air temperature, airplane weight,
and airport elevation, but let us say
that liftoff will occur at 170 mph.
a. Determine the time the
plane takes to go from 0 to 170
mph. (1 mile = 1600 meters)
b. Complete a conservation of momentum diagram showing how the initially stationary
airplane gets to takeoff speed.
event:
initial
final
mass/object/velocity
mass/object/velocity
- 0 +
Momentum conservation equation:
c. Momentum conservation equation:
- 0 +
d. Determine the momentum of the airplane at takeoff.
e. Calculate the impulse the plane receives from the engines during takeoff.

f. What additional information would be needed to calculate the velocity of the exhaust gasses
from the engines